Cremona's table of elliptic curves

6240 = 2⁵ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 13-	Signs for the Atkin-Lehner involutions
Class	6240bf	Isogeny class
Conductor	6240	Conductor
∏ cp	384	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	187388721000000 = 26 · 38 · 56 · 134	Discriminant
Eigenvalues	2- 3- 5- -4  0 13-  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16270,446600]	[a1,a2,a3,a4,a6]
Generators	[-10:780:1]	Generators of the group modulo torsion
j	7442744143086784/2927948765625	j-invariant
L	4.5629126635275	L(r)(E,1)/r!
Ω	0.51644555481218	Real period
R	0.3681343739118	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6240z1 12480bp2 18720l1 31200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240bf1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-	-4	0	-	2	-8	-4	6	8	6	-6	4	-4	6	-8	-10	-4	-8	-14	0	-12	-6	-6

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Quadratic twists for elliptic curve 6240bf1

-4	8	-3	5	13
6240z1	12480bp2	18720l1	31200c1	81120s1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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